In this paper,we will investigate further properties of -schemesintroduced in [Tak].The category of -schemes possessesmany properties of the category of coherentschemes, and in addition,it is co-complete and complete.There is the universal compactification, namely,the Zariski-Riemann space in the categoryof -schemes.We compare it with the classical Zariski-Riemannspace, and characterize the latter by a left adjoint.
Cite this article
Satoshi Takagi, -Schemes and Zariski-Riemann Spaces. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 121–177DOI 10.4171/RSMUP/127-8